<h2>题目编号 : 106</h2>
<div style="color:#666;font-size:80%;">07 October 2005</div><br />
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<p>Let S(A) represent the sum of elements in set A of size <i>n</i>. We shall call it a special sum set if for any two non-empty disjoint subsets, B and C, the following properties are true:</p>
<ol style="list-style-type:lower-roman;">
<li>S(B) <img src='images/symbol_ne.gif' width='11' height='10' alt='&ne;' border='0' style='vertical-align:middle;' /> S(C); that is, sums of subsets cannot be equal.</li>
<li>If B contains more elements than C then S(B) <img src='images/symbol_gt.gif' width='10' height='10' alt='&gt;' border='0' style='vertical-align:middle;' /> S(C).</li>
</ol>
<p>For this problem we shall assume that a given set contains <i>n</i> strictly increasing elements and it already satisfies the second rule.</p>
<p>Surprisingly, out of the 25 possible subset pairs that can be obtained from a set for which <i>n</i> = 4, only 1 of these pairs need to be tested for equality (first rule). Similarly, when <i>n</i> = 7, only 70 out of the 966 subset pairs need to be tested.</p>
<p>For <i>n</i> = 12, how many of the 261625 subset pairs that can be obtained need to be tested for equality?</p>
<p class="info">NOTE: This problem is related to problems <a href="index.php?section=problems&amp;id=103">103</a> and <a href="index.php?section=problems&amp;id=105">105</a>.</p>
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